Electronic test and measurement devices require high precision resistive divider networks, with a high stability of resistance ratios between and among resistors of the networks. To obtain the desired high precision of the resistance ratios, it has been the practice in the prior art to use wire-wound resistors in resistance divider networks because such resistors, although large and expensive to produce, exhibit the desired stability of resistance characteristics with respect to variations in temperature and operating voltage, for example.
However, modern measurement equipment typically utilizes much smaller and less expensive film resistors. Thus, it is desirable to obtain film resistors, whether thin or thick film, which exhibit similar stability in operating characteristics without incurring the additional expense typically associated with the wire-wound resistors or with special selection of film resistors.
A number of factors may influence and alter the ratio of two (or more) resistors formed on a film network. Such factors as:
spatial temperature variation,
temporal variation of film characteristics,
spatial variation of substrate surface condition, and
spatial variation of deposited film characteristics each affect the resistivities, hence resistances, resistance ratios, temperature of coefficient of resistance (TCR) and other characteristics of film resistors.
Because of the non-perfect substrates and non-perfect depositions thereon which form film resistor networks, both the film and the substrate on which it rests have characteristics which vary from area to area. Accordingly, resistors formed at different areas have different characteristics, as above noted. Moreover, however, such differences in characteristics lead to differences in response of the different resistors to external environmental impacts.
For example, when resistors at different locations of the substrate are formed of films with different characteristics, the films tend to oxidize at rates which may differ for the different locations, hence for the different resistors. Accordingly, the characteristics of the resistors will vary with time at different rates, thus providing a time variation in the ratio of the resistances in the network.
For example, it is known that the ratio of resistance between two resistors, R.sub.1 /R.sub.2 for example, varies with time even when measured at a single temperature. Similarly, at any given time, the interface between the deposited film and the substrate will also affect the resistance ratio, as will the temperature distribution along the film network.
As another example, stress and strain applied to the network results in different effects on the different resistors, because of the different characteristics thereof. Thus, application of such external forces will result in undesirable variation in resistance ratio in a network.
Accordingly, it is desired to provide increased stability to such networks in spite of the presence of the above listed factors.
The prior art has attempted to provide a stabilized resistance ratio in a film resistance network by maintaining the mean temperature for two resistors at approximately the same value, thus attempting to provide the same resistivity for the two resistors. For example, it is known that the temperature of material forming a resistor varies with location along the resistor because of power dissipation in the resistor. Accordingly, one known prior art method attempts to provide a common temperature for two resistors by forming one resistor at a location in the proximity of a portion of a second resistor exhibiting an operating temperature corresponding to the mean temperature of the entire second resistor.
More particularly, a location is selected in a linear portion of one linearly distributed resistor, the location exhibiting a temperature which is reasonably expected to equal the mean (average) temperature of the entire resistor. Another resistor is formed at that location, with the first mentioned resistor being formed in two portions, on either side of the second resistor. Thus, the prior art attempts to minimize temperature differences between two resistors and to provide substantially a common temperature for the first and second resistors so that, as operating temperature changes, the actual temperatures of the two resistors will remain substantially equal to one another. Thus, the prior art looks at and attempts to correct an observed effect, the temperature dependent variation of resistance, by correcting a symptom (temperature differences) rather than by correcting an underlying cause of the symptom.
However, such an approach to stabilization of resistance ratios is difficult to carry out, since it is first necessary to determine a point in the first resistor which exhibits a mean temperature of the resistor. Further, the prior art approach is deficient in that it assumes that the TCR for the two resistors is the same and thus ignores variations in resistance caused by variation in TCR characteristics, which is caused by uneven distribution of resistor material. Additionally, the prior art approach is incapable of providing an arrangement of a plurality of resistors, and not just one, which may be used in one or more voltage divider networks with improved precision. Moreover, the above described prior art approach is needlessly complex, since it requires maintaining at the same values the actual temperatures of the two resistors, rather than the simpler task of maintaining a more nearly constant tracking of temperature coefficients of the resistors.
As disclosed in the parent application hereof, which application is hereby incorporated herein by reference, it is sufficient to provide a simple, novel and inexpensive arrangement, which arrangement is also used in the present invention, to obtain a significant improvement in tracking of resistance ratios. More particularly, it is improved tracking of temperature coefficients, rather than tracking the temperatures themselves, which is used in the parent application to obtain a significant improvement in precision and accuracy of film resistance divider networks and thus of measurement and test equipment using such networks.
The reduced complexity of the arrangement provided in the parent application for improving the precision of measuring equipment is due to the recognition of the fact that it is the inconsistency of temperature coefficients, rather than temperature values, which is an underlying cause of poor temperature tracking of resistance ratios. Accordingly, in the parent application it is recognized that improvement of consistency of the TCR is sufficient to achieve highly improved precision of the tracking of resistor ratios, irrespective of the actual operating temperature of the resistors. Indeed, as will be shown in the following description, the concept of the parent application hereof provides a minimum improvement of 885% over the prior art approach which attempts to equalize operating temperatures.
The added difficulty and expense of the prior art approach to obtaining precise matching of actual temperature values is thus unnecessary and fails to obtain the improved accuracy provided even in the parent application.
Unlike the prior art, the invention disclosed in the parent application hereof provides an arrangement of resistor components along the substrate of the network which eliminates differences in TCR between two resistors caused by variations in characteristics of the material forming the resistors as a function of location on the substrate, hereinafter referred to as geographic variations in these characteristics. In the copending parent application, it is recognized that ratio stability for a pair of resistors forming a voltage divider is dependent on three primary factors.
1. TCR tracking, defined as the difference in the temperature coefficient of resistance (TCR) of the resistors making up the divider;
2. VCR tracking, defined as the difference in the voltage coefficient of resistance (VCR) of the resistors; and
3. the difference in the temperatures of the resistors, which is addressed to some extent by the prior art.
In considering the effect of TCR tracking, TCR, which may be positive or negative, is defined as: ##EQU1## where R.sub.2 and R.sub.1 are the resistance values of a single resistor at temperatures t.sub.2 and t.sub.1 respectively.
As noted in the parent application hereof, the TCR tracking factor, determined by the differences in the TCR's of the resistors comprising the network, has a most significant effect on ratio stability. In a two resistor network, if the TCRs of the two resistors comprising the network are identical, the ratio of the two resistors will remain constant as the ambient temperature changes. When the TCRs of the resistors are not the same, the resistance ratio includes a component which varies due to TCR effects. This component of the ratio will change as the ambient temperature changes. The greater the difference in the TCR's of the two resistors, the greater will be the change in the ratio and the poorer will be the ratio stability. By reducing or eliminating such differences, the ratio stability is significantly improved.
In considering the effect of VCR tracking, VCR is defined as: ##EQU2## where R.sub.2 and R.sub.1 are the resistance values of a single resistor at applied voltages E.sub.2 and E.sub.1 respectively.
The VCR of deposited film resistors is always negative, and for well designed, properly manufactured, thin film resistors, the VCR is generally quite low. For example, thin film resistors made from 100 to 200 ohms per square material typically have VCR's in the range of 0.001 to 0.01 ppm/volt. Hence, a 10 megohm resistor will decrease in ohmic value by 1 to 10 ppm (10 to 100 ohms) when the voltage applied thereto is increased by 1,000 VDC (e.g. from 100V to 1100V).
The effect of the VCR on the absolute value of a film resistor is essentially instantaneous while the effect of the TCR on the absolute value of a film resistor depends on the thermal time constant of the resistor. Typically 90% of the temperature rise is complete in less that one minute. The combined effect of VCR and TCR on the resistor value is called the power coefficient of resistance or PCR, and is the algebraic sum of the change in resistance of a resistive element due to an increase in applied voltage as determined by the VCR thereof (always negative) and the change in resistance of the same resistive element due to the self heating caused by the same increase in applied voltage, as determined by the TCR thereof (which may be either positive or negative). The combined effect (PCR) can cause the resistor value either to increase or decrease, or in rare cases, even to remain constant.
In considering the effect of temperature differences between the resistors, the relative temperature of the two resistors depends upon three parameters:
1. the power dissipated per unit area by each resistor;
2. the distance between the two resistors; and
3. the thermal conductivity of the substrate.
As described above, tee prior art does not address these parameters, recognizing only that power dissipation causes an uneven temperature distribution in a resistor and concluding that at some point in a resistor there will be found a location possessing a temperature equal to the mean temperature of the resistor However, such an approach assumes that temperature characteristic of the resistor is uniform along its length. That is, the prior art considers power dissipation, and hence temperature distribution, to be substantially uniform along the resistor, leading to a conclusion that the maximum temperature of a resistor will always be at the center point thereof, i.e., at the point furthest removed from the two end portions of the resistor, which are further assumed always to be at the minimum temperature of the resistor. Thus, it is concluded by the prior art that the average temperature of a resistor will be observed at a point approximately half way between the center point and an end point thereof, i.e., at a point 1/4 the distance between one end portion and the other end portion of a linear resistor.
No consideration is given in the prior art to the fact that materials forming the resistor are inevitably deposited at nonuniform thickness along the substrate, and that for this and other reasons a resistor will thus exhibit one temperature characteristic on one portion of the substrate and another characteristic on another portion. Thus, the attempted approach of the prior art, which fails to correct for or even consider such geographic variations in TCR and which presumes a predetermined point of the resistor to exhibit average temperature for a resistor, is of necessity in error.
However, as noted in the copending parent application, the geographic variation of characteristics of the resistive material is of significance in determining the relative temperatures of two resistors. For example, regardless of the method used to deposit the resistive material on the substrate, there is always some random variation in the metallurgy of the film. Thus, from one edge of the substrate to the opposite edge the TCR of the resulting metal film tends to vary smoothly, although not necessarily linearly, with distance from the reference edge. Hence, it is virtually impossible to have resistors with identical TCR's so that even if the temperatures of two resistors track, the resistances thereof will not because of nonuniformity of TCR.
There has been a long-felt need for a film resistor divider network where the TCR difference of the individual resistors approaches zero over the operational temperature range and the temperature difference of the individual resistors approaches zero over the operational voltage range. As above noted, in the parent application hereof it is recognized that TCR varies from one edge of the substrate to the opposite edge thereof and thus that for different resistors, although precisely formed to have identical dimensions, the TCRs will be different. By providing an arrangement wherein each resistor may be formed as a plurality of resistor portions, and wherein the portions are interleaved in a regular manner, the parent application hereof provides an approach to overcoming the above noted difficulties of the prior art.
However, the approach of the parent application provides more than mere temperature stability. As hereinabove noted, geographic variation occurs in any of the characteristics of the resistance, and not only in the TCR thereof. Accordingly, the resistance ratios of film resistor networks formed on a substrate tend to vary with time and with external environmental factors, such as torque, stress and strain, thermal shock and temperature changes applied to the unit. By providing a layout in which two resistors, for example, undergo the same characteristic variations, in the arrangement disclosed in the parent application the various effects of environmental factors such as externally applied thermal shock, passage of time, and the like, are seen substantially equally by the two resistors. Thus, although the resistances of the two resistors continue to be affected by such factors, the resistance ratio between the two resistors becomes more highly stabilized.
Further, the approach of the parent application sharply reduces the settling time when switching different voltage levels across the netword, such as when switching 100 volts to 1100 volts, for example. There are several reasons for this. First, each of the five high value subelements in a 9 element 2 resistor network dissipate only 1/5 as much as a single high value element in a 2 resistor side-by-side network, hence the temperature rise of each is greatly reduced. Second, being smaller, the subelements reach their maximum temperatures sooner. Third, because of the interleaing, the centers of temperature differentials are greatly reduced. All three factors combine to sharply reduce settling time--a most important consideration in systems applications.
The ultimate reduction in settling time and improvement in TC tracking and ratio stability results when each leg of the serpentine pattern of one resistor is interleaved with each leg of the serpentine pattern of the other resistor. The 9 section arrangement discussed above represents a practical compromise with this ideal.
However, the approach of the parent application overcomes the effects on resistance ratio of variation in TCR and other characteristics only in one direction along a substrate. Although the resultant TCR tracking ratio, for example, is shown in the parent application to improve significantly over the prior art, there remains a need for still further improvement in consistency of resistance ratios and for enhancing tracking of resistance ratios still further for film resistors formed on a substrate, thus to improve ratio stability of voltage divider networks still more significantly than had been previously possible.